Related papers: Hankel Singular Value Decomposition as a method of…
Waveform decomposition is needed as a first step in the extraction of various types of geometric and spectral information from hyperspectral full-waveform LiDAR echoes. We present a new approach to deal with the "Pseudo-monopulse" waveform…
A new statistical model designed for regression analysis with a sparse design matrix is proposed. This new model utilizes the positions of the limited non-zero elements in the design matrix to decompose the regression model into…
Modern imaging techniques for probing brain function, including functional Magnetic Resonance Imaging, intrinsic and extrinsic contrast optical imaging, and magnetoencephalography, generate large data sets with complex content. In this…
By representing documents as mixtures of topics, topic modeling has allowed the successful analysis of datasets across a wide spectrum of applications ranging from ecology to genetics. An important body of recent work has demonstrated the…
Non-parametric representations of dynamical systems based on the image of a Hankel matrix of data are extensively used for data-driven control. However, if samples of data are missing, obtaining such representations becomes a difficult…
Truncated singular value decomposition is a reduced version of the singular value decomposition in which only a few largest singular values are retained. This paper presents a novel perturbation analysis for the truncated singular value…
Disentangling anatomical and contrast information from medical images has gained attention recently, demonstrating benefits for various image analysis tasks. Current methods learn disentangled representations using either paired multi-modal…
In the present study, we demonstrate how to perform, using quantum annealing, the singular value decomposition and the principal component analysis. Quantum annealing gives a way to find a ground state of a system, while the singular value…
Appropriate preprocessing is a fundamental prerequisite for analyzing a noisy dataset. The purpose of this paper is to apply a nonparametric preprocessing method, called Singular Spectrum Analysis (SSA), to a variety of datasets which are…
Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…
Singular value decomposition (SVD) is the mathematical basis of principal component analysis (PCA). Together, SVD and PCA are one of the most widely used mathematical formalism/decomposition in machine learning, data mining, pattern…
This article introduces a new signal analysis method, which can be interpreted as a principal component analysis in sparse decomposition of the signal. The method, called principal basis analysis, is based on a novel criterion:…
The ability to express a learning task in terms of a primal and a dual optimization problem lies at the core of a plethora of machine learning methods. For example, Support Vector Machine (SVM), Least-Squares Support Vector Machine…
Encoding of spectral information onto monochrome imaging cameras is of interest for wavelength multiplexing and hyperspectral imaging applications. Here, the complex spatio-spectral response of a disordered material is used to demonstrate…
In this paper, a fresh procedure to handle image mixtures by means of blind signal separation relying on a combination of second order and higher order statistics techniques are introduced. The problem of blind signal separation is…
We present a mathematically justifiable, computationally simple, sample eigenvalue based procedure for estimating the number of high-dimensional signals in white noise using relatively few samples. The main motivation for considering a…
Singular value decomposition is widely used in modal analysis, such as proper orthogonal decomposition and resolvent analysis, to extract key features from complex problems. SVD derivatives need to be computed efficiently to enable the…
While the acquisition of time series has become more straightforward, developing dynamical models from time series is still a challenging and evolving problem domain. Within the last several years, to address this problem, there has been a…
In this paper, a sparse-based method for the estimation of the parameters of multidimensional ($R$-D) modal (harmonic or damped) complex signals in noise is presented. The problem is formulated as $R$ simultaneous sparse approximations of…
Advances in virtual reality have generated substantial interest in accurately reproducing and storing spatial audio in the higher order ambisonics (HOA) representation, given its rendering flexibility. Recent standardization for HOA…